Gerard ’t Hooft

VSV `Leonardo da Vinci’ Symposium, TU Delft, March 16, 2007

Utrecht University

The electro-magnetic force

J.C. Maxwell 1864

Gravitation

The fourth force:

Gravity is an accumulative force !

All atoms in the Earthpull all atoms in your

body to the same direction (downwards) !

Curved coordinates

time

Coordinateshight

Near a source of gravity (such as the Earth),space and time are curved

General Relativity

There is a “curvature conservation law”

There is also a “matter conservation law”(energy, momentum and forces)

In Einstein’s attempts to find a formula, they did not match !

To make them match, you must assume thatnot only matter (or Energy ) is the source ofgravity, but also pressure !

2/ c

This you will not notice, under ordinary circumstances

negative pressure (tension)

pressure

The total pressure always cancels out !!!

Einstein had to add an extra term to his equation.

12

3

8

E p

GR R g T

grav. source

3E E p

For light, and electro-magnetic fields, 3E p

So, light couples twice as strong to gravity as matter !

Light rays bend twice as much asone might expect !

time

Why does“Dark energy”

make the Universeexpand ? -

Dark energy requiresdark pressurewhich is negative !

3 2

p E

E p E

The Black Hole

Electromagnetism: like charges repel, opposite charges attract → chargestend to neutralize

Gravity: like masses attract → masses tend to accumulate

horizon

Where is the gravitational field strongest? The formation of a Black Hole

even light cannot

escape from within this

region ...

Black Hole

The Schwarzschild Solution to Einstein’s equations

( )2

2 2 222

2 2 2d sid

d 1 d ( )d1

nMr M

r

rs t r q q j= - - + + +

-

Karl Schwarzschild1916

“Über das Gravitationsfeldeines Massenpunktes nachder Einsteinschen Theorie”

As seen by distantobserver

As

experienced by astro-

naut himself

They experience time differently. Mathematics tells usthat, consequently, they experience particles differently

as well

Time stands stillat the horizon

Continueshis waythrough

Stephen Hawking’s great discovery:the radiating black hole

Electro-magnetic radiation

gravitational radiation

The photon has spin = 1

The graviton has spin = 2

Heavy gravitating bodies emit gravitational radiation

In the process, they loose energy: the orbit shrinks

The binary pulsar PSR 1913+16

(Figure from Weisberg et al. 1981)

(Figure from Weisberg et al. 1981)

Orbit shinks 3.1 mm per orbit

Violent events in the cosmos

LISA A gravitational antenna

LIGO Hanford, WaLaser Interferometer Gravitational wave Observatory 4 + 4 km

VIRGO Gascina (near Pisa) 3 + 3 km

LISA

Main Spacecraft

Spacecraft # 3 Spacecraft # 2

Secondaries

photon graviton g

The PhotonSpin = 1 Spin = 2

PP PP

PPPP

PPPP

PP PP

Equal charges repel one another ...

Equal masses attractone another ...

The Graviton

MoonMoon

Moon

Earth

Sun 0 180 360o o o

strength of force This is the wave function of a spin 2 particle

Graviton

Force and spin

The Universal Force Law:

nst 1 22

CQ Q

ForceR

Gravitation:

1 22

M MForce G

R

Distance

ForceMaxwell & YM:

There are two kinds of curvature:

Riemann curvature (space and time near Earth)

Ricci curvature (only inside Earth, the real source of gravity)

Einstein tried a formula: 4 GR T Ricci curvature Matter density

But there was something wrong !

(for a curved piece of paper, these are the same, only in many-dimensional space-time, Ricci is more special.

There is a “curvature conservation law”

There is also a “matter conservation law”(energy, momentum and forces)

In Einstein’s original formula, they did not match !

To make them match, you must assume thatnot only matter (or Energy ) is the source ofgravity, but also pressure !

2/ c

This you will not notice, under ordinary circumstances

negative pressure (tension)

pressure

The total pressure always cancels out !!!

Einstein had to replace by4 GR T

12

12

(3 )

( )8

E p E

R T T gG

grav. source